Graph Neural Networks With Convolutional ARMA Filters

By Filippo Maria Bianchi, Daniele Grattarola, Lorenzo Francesco Livi, Cesare Alippi. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2019

500 citations recorded by the source corpus.

Popular graph neural networks implement convolution operations on graphs based on polynomial spectral filters. In this paper, we propose a novel graph convolutional layer inspired by the auto-regressive moving average (ARMA) filter that, compared to polynomial ones, provides a more flexible frequency response, is more robust to noise, and better captures the global graph structure. We propose a graph neural network implementation of the ARMA filter with a recursive and distributed formulation, obtaining a convolutional layer that is efficient to train, localized in the node space, and can be transferred to new graphs at test time. We perform a spectral analysis to study the filtering effect of the proposed ARMA layer and report experiments on four downstream tasks: semi-supervised node classification, graph signal classification, graph classification, and graph regression. Results show that the proposed ARMA layer brings significant improvements over graph neural networks based on polynomial filters.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f55781f7ce6fd31e946f0efe76d5bf89858391d1

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Citations in the corpus

BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation (2021, methodology): “GPR-GNN, ARMA and ChebNet can learn different filters from the signals.”
How Powerful are Spectral Graph Neural Networks (2022, methodology): “ARMA (Bianchi et al., 2021) uses rational filters.”
SIGN: Scalable Inception Graph Neural Networks (2020, methodology): “We refer the reader to recent review papers Bronstein et al. (2017); Hamilton et al.”
Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View (2019, background): “…(Verma, Boyer, and Verbeek 2018) Convolution GraphSAGE (Hamilton, Ying, and Leskovec 2017) Convolution GAT (Veliˇckovi´c et al. 2018) Attention ARMA (Bianchi et al. 2019) Convolution GraphSAGE (Hamilton, Ying, and Leskovec 2017) Convolution HighOrder (Morris et al. 2019) Attention GGNN (Li et al.…”
Graph Representation Learning (2020, background): “[2018] consider Cayley polynomials of the Laplacian and Bianchi et al. [2019] consider ARMA filters.”
Spectral Clustering with Graph Neural Networks for Graph Pooling (2019, methodology): “…to process graphs with neural networks, including recurrent architec- tures (Scarselli et al., 2009; Li et al., 2016; Gallicchio & Micheli, 2020) or convolutional operations inspired by filters used in graph signal processing (Defferrard et al., 2016; Kipf & Welling, 2017; Bianchi et al., 2019a).”